Question

solve using substitution method x+y=5 and 2x-3y=4

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Answer 1

Answer:-

• $\bf{x = \dfrac{19}{5}}$

• $\bf{y = \dfrac{6}{5}}$

• Given:-

$x + y = 5\: \: \: \: \longrightarrow{\bf{eqn.1}}$

$2x - 3y = 4 \: \: \: \: \longrightarrow{\bf{eqn.2}}$

• To Find:-

Value of:

$x =\bf{?}$

$y =\bf{?}$

• Method:-

$Substitution \: Method$

• Solution:-

$x + y = 5$

→ $x = 5 - y$

• Substituting this value of $\bf{x}$ in $\bf{eqn.2}$:-

We have,

→ ${2(5-y) - 3y = 4}$

→ ${10 - 2y - 3y = 4}$

→ ${10 - 5y = 4}$

→ ${5y = 10 - 4}$

→ ${5y = 6}$

→ $\bf{y = \dfrac{6}{5}}$

• Substituting $\bf{y = \dfrac{6}{5}}$ in $\bf{eqn.1}$:-

We have,

→ $x + \dfrac{6}{5} = 5$

→ $x = 5 - \dfrac{6}{5}$

→ $x = \dfrac{25 - 6}{5}$

→ $\bf{x = \dfrac{19}{5}}$

$\large\therefore$ Therefore,

• $\bf{x = \dfrac{19}{5}}$

• $\bf{y = \dfrac{6}{5}}$

Answer 2

Step-by-step explanation:

GIVEN:

X+Y=5 AND 2X-3Y=4.

TO FIND:

VALUE OF X AND Y.

X+Y=5 ======> EQUATION 1.

2X-3Y=4======> EQUATION 2.

METHOD TO BE USED:

SUBSITUTION METHOD.

ALGORITHM OF THIS METHOD:

STEP 1. FIRST FROM ANY EQUATION 1 AND 2 EXPRESS X IN TERMS OF Y.YOU CAN ALSO EXPRESS Y IN TERMS OF X.

STEP 2. THEN PLUG THAT EXPRESSION INTO ANY OF EQUATION 1 AND 2 BUT NOT THE YOU SOLVE IN STEP 1.

STEP 3. THEN AFTER GETTING VALUE IF X OR Y ,SUBSTITUTE THIS VALUE TO ANY OF THESE EQUATIONS.

SOLUTION:

SOLVING EQUATION 1.

X+Y=5=>X=5-Y

PLUGGING THIS EXPRESSION TO EQUATION 2.

2X-3Y=4

=>2(5-Y)-3Y=4

=>10-2Y-3Y=4

=>10-5Y=4

=>-5Y=4-10=-6

MINUS -MINUS CANCELLED OUT, WE GET

5Y=6

=>Y=6/5

NOW SUBTITUTING THIS VALUE TO EQUATION 1.

X+Y=5

=>X+6/5=5

=>5X+6/5=5

=>5X+6=5×5=25

=>5X=25-6=19

=>X=19/5

HENCE THE VALUES OF X AND Y ARE

19/5 AND 6/5 RESPECTIVELY.